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Optimal list order under partial memory constraints

Published online by Cambridge University Press:  14 July 2016

Y. C. Kan and
S. M. Ross
Y. C. Kan*
Affiliation:
University of California, Berkeley
S. M. Ross*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Operations Research Center, University of California, Berkeley, CA 94720, U.S.A.
∗ Postal address: Operations Research Center, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

Suppose that we are given a set of n elements which are to be arranged in some order. At each unit of time a request is made to retrieve one of these elements — the ith being requested with probability Pi. We show that the rule which always moves the requested element one closer to the front of the line minimizes the average position of the element requested among a wide class of rules for all probability vectors of the form P 1 = p, P 2= · ·· = Pn = (1 – p)/(n − 1). We also consider the above problem when the decision-maker is allowed to utilize such rules as ‘only make a change if the same element has been requested k times in a row', and show that as k approaches infinity we can do as well as if we knew the values of the Pi.

Keywords

OPTIMAL LIST ORDERMEMORY CONSTRAINTSTRANSPOSITION RULEk-IN-A-ROWRANDOMIZATIONTIME REVERSIBILITY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980, pp. 1004 - 1015
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research partially supported by the Office of Naval Research under Contract N00014–77–C–0299 and the Air Force Office of Scientific Research (AFSC), USAF, under Grant AFOSR–77–3213B with the University of California.

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